Inverse portfolio problem with coherent risk measures

Inverse portfolio problem with coherent risk measures

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Article ID: iaor201530455
Volume: 249
Issue: 2
Start Page Number: 740
End Page Number: 750
Publication Date: Mar 2016
Journal: European Journal of Operational Research
Authors: ,
Keywords: optimization, risk, financial, decision
Abstract:

In general, a portfolio problem minimizes risk (or negative utility) of a portfolio of financial assets with respect to portfolio weights subject to a budget constraint. The inverse portfolio problem then arises when an investor assumes that his/her risk preferences have a numerical representation in the form of a certain class of functionals, e.g. in the form of expected utility, coherent risk measure or mean‐deviation functional, and aims to identify such a functional, whose minimization results in a portfolio, e.g. a market index, that he/she is most satisfied with. In this work, the portfolio risk is determined by a coherent risk measure, and the rate of return of investor’s preferred portfolio is assumed to be known. The inverse portfolio problem then recovers investor’s coherent risk measure either through finding a convex set of feasible probability measures (risk envelope) or in the form of either mixed CVaR or negative Yaari’s dual utility. It is solved in single‐period and multi‐period formulations and is demonstrated in a case study with the FTSE 100 index.

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